Method and apparatus for very-low-frequency radio nagigation

ABSTRACT

Disclosed is a method and apparatus for improving the accuracy of navigation by the Omega Navigation System. The improvement in the method of navigating by the Omega system relates to the detection of the phase of each of at least two very-low frequency signals and the generation therefrom of a composite signal which bears a predetermined relationship to the detected signals and the predetermined relationship is selected to reduce the positioning error attributable to diurnal variations and geophysical anomalies in the transmission times of the respective signals, and included is apparatus for practicing the method.

United States Patent Pierce Oct. 3, 1972 [54] METHOD AND APPARATUS FORVERY-LOW-FREQUENCY RADI NAGIGATION J .A. Pierce; Radux Cruft Lab.,Harvard University, Cambridge, Mass. Tech. Rep. No. 17 (July 1947) W. H.Guier & G. C. Weifienbach; A Satellite Doppler Navigration SystemProceedings Vol. the IRE, Vol. 48, pp. 507- 516 (April 1960) G. C.Weiffenbach; Measurement of-the Doppler Shift of Radio TransmissionProceedings of the IRE, Vol 48, pp. 750- 754 (April 1960) PrimaryExaminer-Rodney D. Bennett, Jr.

Assistant ExaminerT. I-I. Tubbesing Attorney-Robert G. Crooks, Tennes I.Erstad and J efierson Ehrlich [5 7] ABSTRACT Disclosed is a method andapparatus for improving the accuracy of navigation by the OmegaNavigation System. The improvement in the method of navigating by theOmega system relates to the detection of the phase of each of at leasttwo very-low frequency signals and the generation therefrom of acomposite signal which bears a predetermined relationship to thedetected signals and the predetermined relationship is selected toreduce the positioning error attributable to diurnal variations andgeophysical anomalies in the transmission times of the respectivesignals, and included is apparatus for practicing the method.

13 Claims, 9 Drawing Figures e 2e PHASE LOCAL-TIME PHASE DETECTOR 44REFERENCE DRIVER 5e DETECTOR EXCITATION SERVO AMPLIFIER AMPLIFIER (0.2Kc/s [0.2 Kc/s J L [3.6 Kc/s 58. I36 Kc/s 6O. PHASE SHIFTER SERVO MOTORFS/ERVO MOTOR P PHASE SHIFTER 84 as Ion i H A l=m 3 72 2=|5 l 7 l 62 i-P 95 82 2= L I 98 I2 we as re (m-l)=l ao 74 I no I04 I30" I24 Ioa [28I02 COMPOSITE A All INDICATOR INDICATOR I we 68 COMPOSITE 6B A-& A"-e"INDICATOR INDICATOR INDICATOR PAIENIEIIIJBI 3 I972 TRANSMISSION TIME INIO.2 Kc/s CENTICYCLES SHEET 1 [IF 6 COMPOSITE (m=9/4) NORWAY inCAMBRIIDGE SUNRISE AT NORWAY 5 26 DECEMBER 1567' I874O I I I 0 I2 GMTTIMES OF ARRIVAL OF SIGNALS FROM NORWAY JOHN A. PIERCE INVENTOR BY W1ATTORNEY HAWAII AT CAMBRIDGE 8 JULY MEAN. 7 JUNE 9 JULY I968 COMPOSITEm=3 O=5.9

COMPOSITE m=9l4 O'=2.7 27900 lOI 27800 TIME OF TRANSMISSION INCENTICYCLES 0F IO.2 Kc/s 0 2 4 6 8 IO I2 I4 l6 I8 20 22 24 GMT F/G 2JOHN A. PIERCE INVENTOR BY WH- m ATTORNEY PAIENIEIIBCTS 1912 SHEEI 3 [IF6 g} I l I l I I I I I I l I I l I I l l I I I .J HAWAII AT CAMBRIDGE5'20 DECEMBER I967 g 27980- 2 L JI'II' "3n "I 5 EPIC" 27960 5 COMPOSITE(m=9/4) z 27 0-; i Q 27840 :=.2;.'-?.' 1' e;

Ir a; r w 1 0 9 27820 |o.2 Kc/s =g Q z a: 4 B3 S 5 27800-3 E g1 22 2 33?, 33 d I: 780 Lu 9 in. a Z I"- (BIZ I; 9 27760- g? III I) 4 I: 5:." 3.I 5 27740 g w 0 (D D i 1 1 P1 1 l 1 l 1 a r I E O 2 4 6 8 IO l2 I4 I6 [820 2 24 GMT F/G 4 TIMES OF ARRIVAL OF SIGNALS FROM HAWAII 8 NORWAY ATCAMBRIDGE 8 ////,I\ u r\\ V//7/I\ 1 k Wm: r\\ m: L WAY I\ DAY NIGHT O\ u34 Kc/ Z I? +20 IIII o COMPOSITE T 2 ---20 a: 215

g "40 IO.2 Kc/s DJ 2 00 I2 00 I2 00 I2 00 I2 00 I2 00 FIG 5 NOV 2, I9673 4 s s DEVIATIONS OF THREE TIMES OF ARRIVAL OF SIGNALS FROM NORWAY WITHRESPECT TO THE NORMAL DIURNAL VALUES, FOR A FEW DAYS IN NOVEMBER,

I967, DURING A POLAR CAP ANOMALY JOHN A. PIERCE INVENTOR ATTORNEYPATENTED 967 3 4972 SHEET 5 OF 6 102055 @0205; l Aw Q2 Aw E6828 52052.$205; m9 E6828 mm.

Kuhn: Im uw In EOPOE O mmw JOHN A. PIERCE INVENTOR BY W S 7 ATTORNEYPATENTEIIUCT3 I972 STANDARD DEVIATION OF THE TIME OF ARRIVAL IN |O.2KC/S CENTICYCLES O N 0 SHEET 6 BF 6 2| OCT. 8 NOV.

I4-3I JULY STANDARD DEVIATION OF THE TIME OF ARRIVAL IN IO.2 KC/ SCENTICYCLES 24-HOUR MEANS NORWAY AT CAMBRIDGE I I I NORWAY AT CAMBRIDGE22OCT-8 NOV. I96 7 MENTOR. JOHN A. PIERCE METHOD AND APPARATUS FORVERY-LOW- FREQUENCY RADIO NAGIGATION This invention relates to radionavigation and is particularly directed to methods and apparatus fornavigation by means of very-low-frequency (VLF) radio signals.

As the density of intercontinental transportation increases, the needfor more precise navigation techniques also increases. Precisenavigation is necessary to permit the navigator to select and follow themost direct route and to avoid collision with other ships or aircraft.Celestial navigation techniques have been employed for hundreds of yearsand permit a navigator to determine his position within about fivemiles. However, since these techniques require a clear view of severalstars, celestial navigation techniques cannot be used when the sky isovercast. To overcome this problem, various navigation techniques havebeen proposed using radio frequency signals. Some of these techniques,such as radar, are quite accurate but require tremendous power toachieve significant range. Thus, typical airborne radar units have arange of only about 300 miles; and even the gigantic units of theBallistic Missile Early Warning System have a range of only about 1,000miles. Other radio navigation systems, such as VOR, are limited toline-of-sight ranges; while still others, such as ADF, are stronglyeffected by atmospheric disturbances. Quite recently, avery-lowfrequency navigation system, called Omega, has been introducedwhich overcomes many of these problems. The Omega Navigation System isdescribed in a publication entitled Omega, a World Wide NavigationalSystem dated May 1, 1966 (Defense Document Center No. Ad-630 900). Underthe Omega system, it has been found that very-lowfrequency radio signalscan be reliably transmitted over many thousands of miles with relativelymodest power requirements, and that the time of transmission of suchsignals is predictable with errors of only a few microseconds. Hence, byproviding a network of four transmitting stations (soon to be expandedto eight) at widely-spaced locations about the earth, each carefullysynchronized with the others and each transmitting several time-sharedfrequencies in predetermined sequence, a navigator, located anywhere inthe world, can receive signals from several of these stations, and, byphase-analyzing the signals, can determine his position. Unfortunately,the signals of the Omega system are subject to significant diurnalvariation in the velocity of propagation and the compensation for this,which is proportional to distance, ordinarily leaves residual errors ofone to two miles in position. For instance, Air/Surface Omega NavigationCharts are published by the U. S. Naval Oceanographic Office,Washington, D. C. (a typical chart for the North Atlantic Ocean EasternUnited States is Chart No. V030- 22). The chart indicates isophase lineswith respect to each of the active Omega stations. When a navigatorpositions himself, as in a channel or lane between respective isophaselines, he knows that his distance from a respective transmitting stationis some whole number of cycles or wave lengths of the frequency he isreceiving plus some percentage of a cycle of the respective signal. Byplotting the percentage of the cycle with respect to the laneboundaries, i.e., the isophase lines, the navigator places himself on ahyperbolic line which is parallel to the lane boundaries. By a similarplot with respect to a second station, a second hyperbolic line ofposition is obtained which intersects the first hyperbolic line, thusprecisely pinpointing the location of the receiver. This means that anavigator needs only to identify with respect to a single frequencytransmitted by a respective station, a percentage of one full cycle of awave to determine his position with respect to the lane boundaries. Thelane boundaries correspond to the wavelength of a full cycle of the waveof the respective frequency. It is apparent, therefore, that thetransmission time of a wave can be stated in terms of phase. The periodof a cycle of a 10 Kc/s wave is microseconds. One centicycle is definedas l/l00 of a cycle, and for a 10 Kc/s wave one centicycle equals 1microsecond. Since there is substantial noise in the spectrum at 10Kc/s, a basic frequency of 10.2 Kc/s is used, and phase and transmissiontime readings are expressed in the Omega system in the unit ofcenticycles of 10.2 Kc/s.

The very-low-frequency waves transmitted by an Omega station areeffectively contained in a waveguide which is bounded on one side by theearth and on the opposite side by the lower reaches of the ionosphere.Since the earth and ionosphere are substantially concentric, curved,parallel surfaces, the transmitted waves are reflected between the twosurfaces as. they travel through the wave guide. While the velocity ofan electromagnetic wave transmitted in a vacuum is theoretically equalto the speed of light, regardless of the frequency, the effectivevelocity, that is the speed at which a wave travels from one point onthe earths surface to a second point, will vary from one frequency tothe next. In its simplest terms, this phenomenon is explained by thefact that an electromagnetic wave of one frequency is not reflected bythe ionosphere at the precise level that an electromagnetic wave of asecond frequency is reflected, thus the path traveled by a wave of onefrequency between successive points on the earth is longer than the pathtraveled by the wave of the other frequency.

It is also known that the height at which the ionosphere stands abovethe earth is greater at certain times than it is at other times. Forinstance, the ionosphere is lower at night, thus the travel time of anelectromagnetic wave of a given frequency and between two points on theearths surface is greater during the day than at night. For instance,the average plots of the transmission time of a 10.2 Kc/s signal, asshown in FIG. 3, vary in substantially the same manner each day, subjectto the exceptions listed below.

Certain changes in the effective velocity between two points on theearths surface occur in substantially the same manner each day. Changesin the height of the ionosphere between night and day are typicalexamples. These changes are called diurnal changes. Other, similarchanges in the height of the ionosphere occur between seasons of theyear. The diurnal changes and the seasonal changes described repeat sonearly exactly over the time periods set forth that their effect on theeffective velocity of propagation is predictable, and tables areavailable for use by navigators whereby the readings made by thenavigator are corrected for the effects of diurnal and seasonal changesby reference to a table which provides diurnal and seasonal correctionfactors. A typical table of this type is the Omega Skywave CorrectionTable, US. Navy Oceanographic Office, Washington, D. C. The tableidentified as Publication N 224 (Ill-C) is for Station C (Hawaii) of theOmega System. Using the Omega system with corrections, a resolution of[-2 miles is obtainable. Greater accuracy is still desired, however, andcertain unpredictable geophysical anomalies occur which disrupt thetransmission times of the VLF waves and can cause substantial errors inthe navigators readings. Sudden ionospheric disturbances and polar capanomalies are two of the geophysical anomalies of the type described.

A polar cap anomaly occurs when energetic particles from the sun, mostlyprotons, are precipitated over the polar regions where they causeenhanced ionization. The enhanced level of ionization produces the sameeffect as lowering the level of the ionosphere, thus producingunpredictable changes in the effective velocity of a very low frequencywave. The polar cap anomaly is related, apparently, to sun flares andare generally thought of as being of fairly long duration, i.e., severalhours to several days. FIG. illustrates an example of a polar capanomaly.

The second type of geophysical anomaly, the sudden ionosphericdisturbance, is a similar occurrence, but may occur at any point in theionosphere and not just positioned with respect to the polar caps. Thesudden ionospheric disturbance again produces an enhancement ofionization in the ionosphere related, apparently, to sun activity, andthis type of disturbance also acts to effectively reduce the level ofthe ionosphere in the location of the disturbance. Usually suddenionospheric disturbances are of fairly short duration, i.e., 1 hour, andare believed to effect the geomagnetic lines of force about the earth.In any event, the sudden ionospheric disturbance causes additional,unpredictable changes in the effective velocity of electromagnetic wavesbetween two points on the earth. An example of readings taken during asudden ionospheric disturbance is curve 100 of FIG. 2.

Geophysical anomalies, therefore, act to alter the effective velocityand thus the phase of the signals received by a navigator, and the phasechange will usually result in navigational errors of several miles, andthe error may occur in readings taken over a span of several days.

These disadvantages of the prior art are substantially overcome with thepresent invention, and a novel navigation technique is provided whichemploys the signals of the Omega system to provide significantly moreprecise navigation than has been possible heretofore, while especiallyreducing the effects of sudden ionospheric disturbances and polar capanomalies.

Alternatively, the present invention can be used to minimize or removethe necessity for making diurnal and annual corrections to the observedreadings, as is necessary under the prior art. This version of thetechnique of the present invention offers only a small improvement inaccuracy, but permits a great simplification in the use of Omega.

The advantages of the present invention are preferably attained byobserving signals of at least two frequencies broadcast from each of atleast three appropriate ones of the Omega transmitting stations in termsof a common local reference, processing said signals to derive acomposite signal corresponding to each received station, and employingthe composite signals to determine position.

Accordingly, it is an object of the present invention to provide animproved navigation technique.

Another object of the present invention is to provide an improvedtechnique for navigation by means of very-low-frequency radio signals.

A further object of the present invention is to provide an improvedtechnique for navigation by means of signals broadcast by Omega systemtransmitting stations.

An additional object of the present invention is to provide a techniquefor improving the accuracy and reliability of navigation by suitablyprocessing signals broadcast by Omega system transmitting stations.

A specific object of the present invention is to provide a technique fornavigation wherein signals of at least two frequencies are observed interms of a common local reference for each of at least three appropriateones of the Omega transmitting stations, the received signals areprocessed to derive a composite signal corresponding to each of thereceived Omega Transmitting stations, and the composite signals areemployed to determine position.

An additional object of the present invention is to provide a techniquefor simplifying the operation of Omega navigation by removing therequirement for compensation of observed readings for variations in thevelocity of propagation at various times of the day or year.

These and other objects and features of the present invention will beapparent from the following detailed description taken with reference tothe figures of the accompanying drawing.

In the drawing:

FIG. 1 is a diagrammatic representation showing the ideal distributionof Omega system transmitting stations about the world.

FIG. 2 is a series of graphs of the times of transmission of signals,including three of the composite signals of the present invention, fromHawaii to Massachusetts.

FIG. 3 is a graph showing times of arrival of one of the compositesignals of the present invention and the 10.2 kc/s signal from theNorwegian Omega station.

FIG. 4 is a graph showing times of arrival of one of the compositesignals of the present invention and the 10.2 kc/s signal from theHawaiian Omega station.

FIG. 5 is a graph showing deviations in the times of arrival of an OmegaSystem signal caused by a longterm geophysical anomaly, together with agraph of a difference signal (3.4 Kc/s) and composite signals.

FIG. 6 is a diagrammatic representation of apparatus for performing thenavigation method of the present invention.

FIG. 7 is a diagrammatic representation of the computer of the apparatusof FIG. 6.

FIG. 8 is a graph of the standard deviation of the time of arrival atCambridge of an Omega System signal from Norway at various times of theyear.

FIG. 9 is a graph similar to FIG. 8, but showing the standard deviationof the time of arrival in an Omega System signal at various times of theday.

As seen in FIG. 1, the Omega navigation system calls for locating aplurality of very-low-frequency radio transmitting stations A, B, C, D,E, and F at widelyseparated points about the world. At present, foursuch stations are in operation, located at Hawaii, New York, Norway andTrinidad, and a total of eight is planned. Each of these stations iscarefully synchronized to Greenwich Mean Time, and each transmitscontinuous wave signals at 10.2 kc/s and 13.6 kc/s at specific times.Following the Omega technique, the navigator tracks the phases of the10.2 kc/s signals from three or more of these stations to determine hisposition. If ambiguity is operationally serious, the navigator employsthe 13.6 kc/s signals in a similar manner and compares his position asdetermined by the 13.6 kc/s signals, or as determined by a 3.4 kc/sdifference signal that results from intercomparison of the 13.6 and 10.2kc/s signals.

In accordance with the present invention, it has been found that theaccuracy of position determination may be significantly increased. Toaccomplish this, the times of arrival of both signals from three or moreOmega transmitting stations are observed with respect to a common, localreference and are employed to derive a composite signal having atransmission time which is preferably the mean of the average of thetransmission times of the two Omega carrier-frequency signals and thetransmission time of the difference frequency.

In the curved waveguide without lateral boundaries that is formed by thesurface of the earth and the lower ionosphere, very-low-frequencyelectromagnetic waves may be considered to be propagated in a series ofnormal modes of vibration, of which one mode will be dominant over alarger distance. Several texts have been written, dealing specificallywith this mode phenomenon. For instance, Introduction to TheoreticalPhysics by Leigh Page, published by Van Nostrand Co., New York; Fields &Waves in Modern Radio by Ramo- Whinnery, published by John Wiley & Sons,Inc., New York; Electromagnetic Waves in Stratified Mediums by James R.Wait, published by The National Bureau of Standards and distributed byMacMillan and Co., New York.

In Page, at 222, it is stated that the effective velocity of wavepropagation of a single wave is defined as the phase velocity (Vp). If,however, dispersion exists in a medium through which waves are passing,that is, if the phase velocity is different for different wave lengths,then one of the two sets of waves travels faster than the other andreinforcement and interference take place as the first set gains on thesecond. The velocity with which the regions of reinforcement orinterference advance is known as the group velocity (Vg). The text byWhinnery utilizes the phase (Vp) and group (Vg) velocity concept todevelop a treatment of transverse magnetic waves between parallelplanes. Mr. Whinnery, in his discussion at page 328, develops equationsfor group and phase velocities as follows:

where Vp phase velocity in the waveguide Vg group velocity in thewaveguide, and

V= the effective velocity of propagation of a wave in the mediumcontained in the waveguide.

f cut off frequency f basic frequency At frequencies where theattenuation is low, T, and T, differ only slightly and we may say,without serious error, that In the frequency region from f to f asatisfactory expression for the general phase velocity is the mean ofthe velocities at the two frequencies. (f, and f are two respective VLFtransmitted frequencies, for instance 10.2 Kc/s and 13.6 Kc/s.) Thisstatement leads to the reciprocal relation p 1+ 2/ (5) where T and T arethe transmission times at the lower and higher carrier frequencies,respectively.

The total phase shift along a transmission path at the differencefrequence (f -f is the difference between the two phase shifts at thecarrier frequencies. That is,

( e-1 total phase change along the transmission path at the differencefrequency,

(# the same at the higher carrier frequency, and

dz, the same at the lower carrier frequency.

For each phase shift f f (7) where f frequency.

With these substitutions, Eq. (6) becomes f2 2 f 1 1 d TB 12-1.

where T transmission time for the difference frequency, f the lowercarrier frequency, and f the higher carrier frequency. Inserting thevalues from Eq. (5) and Eq. (8) in Eq.

12+ T. 11. f1 T.

which reduces to where T, Transmission time of the composite signal 'lTransmission time of the lower frequency signal (10.2 kc/s) T,Transmission time of the higher frequency signal 13.6 kc/s) m is aconstant which may have any value but for optimum cancellation ofpropagational anomalies at the Omega frequencies of 13.6 kc/s (f2) and10.2 kc/s (f,), m, is approximately equal to the ratio 9/4. (Where m isthe specific value of m for the frequencies considered.)

The proper value for the ratio m was determined originally by thecorrelation and analysis of experimental data. For instance, FIG. 8shows the standard deviation of the time of arrival in 10.2 kc/scenticycles for signals received at Cambridge, Mass, from the NorwegianOmega station. In this figure, seasonal changes of the standarddeviation time of arrival of an Omega signal are plotted with respect toalternative values of m. It is apparent that for values of m lying in arange between 0 and 5, that the least amount of deviation occurs when m9/4. Similarly, in FIG. 9, the standard deviation of the arrival time ofan Omega signal from the Norway station is plotted against in to reflectdiurnal variations. Again, the least variation occurs when m 9/4.

As previously stated, distance is equal to the transmission timemultiplied by the effective velocity of propagation. Presumably, theeffective velocity of propagation for the composite signal is nearly thevelocity of light. However, it is not convenient to measure distances atthe average height of the energy flow in a curved waveguide withoutlateral boundries, such as that formed by the surface of the earth andthe lower ionosphere. Nevertheless, a close approximation to thevelocity of propagation can be obtained from the expression where c thevelocity of light v the velocity of propagation of the composite signalI: the height of the ionosphere layer a the radius of the earth, 6,370km.

Adopting the customary estimates of 70 km. and 90 km. for the daytimeand night-time heights of the ionosphere layer at very-low-frequencies,we find the ratio of c/v to be about l.0037 for daytime and 1.0047 fornight-time.

This residual diurnal variation can be reduced or removed by using asomewhat larger value of m than the value defined in Equation (1 l Thishas the effect of increasing the transmission time of the compositesignal slightly, and increasing it more by day than by night.

The optimum value of m for cancellation of diurnal variation can beshown both theoretically and experimentally to be in the region near3.25 or 3.5, for the Omega frequencies I02 and 13.6 kc/s. As statedabove, increasing m above the value of m given by Equation (ll) resultsin increased random variation because of imperfect cancellation ofanomalies of propagation. The best value of m for reduction of bothdiurnal and random variation is therefore somewhat less than the value3.25 or 3.5 mentioned above. Experiments indicate that a value of 3.0(for the frequencies 10.2 and 13.6 kc/s) gives approximately the bestoverall reduction of diurnal variation, because it reduces the diurnalefl'ect to a small value without increasing random errors as much aswould occur for exact compensation of diurnal variation.

This alternative technique for the use of composite signals offers theopportunity to navigate without the use of extensive tables of diurnalcorrections, as has been required by the prior art. The resultant errorsare not as small as they can be made by the use of the preferred valueof m together with correction tables, but are as small or smaller thanthe errors under the techniques of the prior art, and the ease ofoperation is greatly increased with accompanying reduction in theopportunity for an operator to make mistakes.

To illustrate the cancellation of propagational anomalies, it has beenreported that, during a sudden ionospheric disturbance, both the normaldaytime variation of the transmission time and the average amplitude ofthe phase advance have magnitudes at 13.6 kc/s which are 0.56 i 0.02 ofthe corresponding magnitudes at 10.2 kc/s. However, in Equation (12)with T indicating a change in T if T is taken as 5 T,/9, it will be seenthat T is zero. Hence, it is clear that one of the results of using thecomposite signal of the present invention is to substantially eliminatethe effects of sudden ionospheric disturbances.

For example, FIG. 2 shows the variation in the time of arrival of a 10.2kc/s signal, curve 100, and a 13.6 kc/s signal curve 101, from Hawaii,for alternate values of m. In curves I00 and 101 the solid lines aredrawn through observed values on July 8, 1968; a day on which a majorsudden ionospheric disturbance occurred at about 17' 10" GMT. The dottedcurves 102, 103 are drawn through averages of the anticipatedtransmission times taken over an extended period. The sudden decrease inthe time of arrival beginning at 17" 10'" is similar at 13.6 kc/s and at10.2 kc/s, but is smaller at 13.6 kc/s. At the difference frequency of3.4 kc/s (m 4), curve 104, the effect is reversed, and an increase intransmission time is shown at the time of the sudden ionosphericdisturbance.

The composite signal, curve 105, with m 9/4 shows almost no effect atthe time of the sudden ionospheric disturbance. For this value of m theoverall agreement between the solid and the dotted lines is the best.There is, however, a residual diurnal variation.

When m 3, as in curve 106, these characteristics are reversed. Theaverage dotted curve 107 shows very little diurnal variation, but thesudden ionospheric disturbance produces a delay in the transmissiontime, although one only about one-third as large as the effect at 10.2kc/s. Similarly, as seen in FIG. 3 (for signals from the Norwegian Omegastation) and FIG. 4 (for signals from the Hawaiian Omega station), thediurnal variation of the composite signal of the present invention issignificantly smaller than for the 10.2 kc/s signal. FIG. shows curvesfor the 3.4 kc/s Omega difference signal, the 10.2 kc/s Omega signal,and the composite signal of the present invention transmitted from theNorwegian Omega station and measured at Cambridge, Mass, during a polarcap anomaly of fairly large magnitude. It will be apparent, in FIG. 5,that the deviations of the 3.4 kc/s difference signal are a slightlyreduced, mirror image of the deviations of the 10.2 kc/s signal, whilethe deviations of the composite signal of the present invention offer agreat improvement in stability.

In the form of the present invention chosen for purposes ofillustration, FIG. 6 shows an antenna 2 positioned to receive thevery-low-frequency radio signals broadcast by the Omega transmittingstations. As shown, an antenna 2 receives signals at a first frequency,such as 10.2 kc, transmitted from each of the transmitting stations insequence. These signals are amplified by amplifier 4, and passed tomixer 6 and phase detector 8. Similarly, antenna 2 receives signals at asecond frequency, such as 13.6 kc, transmitted from each of thetransmitting stations in sequence, and these signals are amplifier byamplifier l0, and passed to mixer 12 and phase detector 14. A local,accuratefrequency source 16, generates a signal at 3,400cyclesper-second which is passed through a suitable divider circuit 18to drive a pulse circuit 20 yielding a pulsetype signal at a frequencyof 1,133.33 cycles-persecond which is applied to filter circuits 22, 24,and 26. Filter 22 passes the eighth harmonic of the pulse-type signal,having a frequency of 9,066.66 cycles-persecond, to mixer 6. Similarly,filter 24 passes the eleventh harmonic of the pulse-type signal, havinga frequency of 12,466.66 cycles per second, to mixer 12. Filter 26removes the harmonics from the pulse-type signal and passes the 1,133.33cycle-per-second signal to the local-time reference driver 28. Thedriver 28 is simply an amplifier which serves to provide sufficientpower to drive the respective phase shifters 60, to which it is coupled.The signals from both phase detectors 8 and 14 and from local-timereference driver 28 are supplied to a suitable computer 29. The computer29 pairs each of the signals from phase detector 8 with thecorresponding signal from phase detector 14 so that the signalsoriginating at each of the transmitting stations are paired. Thecomputer 29 then processes each of the pairs of signals, in conjunctionwith the signal from the local-time reference driver 28, in the mannerdescribed above, and derives a plurality of signals, each having a valueindicative of the distance to a respective one of the transmittingstations, which are supplied to indicator means 68 to provide a visualposition indication for the navigator.

Obviously, numerous types of computers can perform the functions ofcomputer 29. However, to insure sufficiency of disclosure, one suchcomputer is disclosed in FIGS. 6 and 7. As shown, computer 29 is anelectro-mechanical computer wherein the signals from pulse circuit 20are also supplied to a second divider circuit 30 which yields a drivingsignal having a frequency of 56.66 cycles per second. The driving signalis passed through a suitable filter 32 and is applied, via conductor 34,to motor excitation amplifier 36 and, via conductor 38, to commutatoramplifier 40 and, hence, to commutator 42. Commutator 42 suppliessignals to energize servoamplifiers 44 and 46 and also supplies signalsto switching means 48. For each transmitting station, a separatemotor-phase-shifter unit, as shown in FIG. 7, is provided and each ofthese motor-phase-shifter units includes a respective portion for eachof the frequencies to be received. For simplicity, four suchmotor-phase-shifter units have been represented in FIG. 6, eachrepresented by a pair of blocks A and A, B and B, C and C, and D and D.-It will be seen that the unprimed blocks A, B, C, and D represent thatportion of the respective motonphaseshifter unit which responds to the10.2 kc/s signal from the corresponding Omega transmitting station,while the primed blocks A, B, C, and D represent that portion of therespective motor-phase-shifter unit which responds to the 13.6 kc/ssignal from the corresponding Omega transmitting station. Switchingmeans 48 serves to position switches 50, 52, 54, and 56 to apply thesignals passed thereby to the appropriate one of the motor-phase-shifterunits. Phase-shifter driver 28 is connected to all of the phaseshifters, while motor-excitation amplifier 36 is connected to all of themotors.

All of the motor-phase-shifter units 58, 60 (FIG. 6) are identical.However, for simplicity, only motor phase shifter A-A has been shown. Asseen in FIG. 7, each rnotor-phase-shifter unit comprises two motors 58and 58' and two phase shifters 60 and 60'. Motors 58 and 58 both receiveexcitation current from excitation amplifier 36. However, the speed ofmotor 58 is determined by the 10.2 kc/s signal from the respective Omegatransmitting station A which is applied to motor 58 through servoamplifier 44 and switch 54. Phaseshifter driver 28 applies a local-time,reference signal to both phase shifters 60 and 60'; while a signalindicative of the phase of the 10.2 kc/s signal is applied from phaseshifter 60 to phase detector 8 through switch 50, and a signalindicative of the phase of the 13.6 kc/s signal is applied from phaseshifter 60' to phase detector 14 through switch 52. Since it isdesirable to indicate the transmission time of each of the signals as apercentage of a period of the 10.2 kc/s signal, the input of phaseshifter 60 is multiplied by 10 through gears 62 and 64 over the speed ofthe drive input shaft 66 of a suitable indicator 68 that indicates thearrival time of the 10.2 kc/s signal from Omega station A. Likewise, theinput of phase shifter 60 is multiplied by 7 /2 through gears 70 and 72above thespeed of the drive input shaft 74 of indicator 68 thatindicates the arrival time of the 13.6 kc/s signal from Omega station A.As has been previously shown the transmission time for the compositesignal is equal to m times the transmission time at 13.6 kc/s minus(m-l) times the transmission time at 10.2 kc/s. To obtain this, motor 58drives shaft 76 at a rate of 20 times the rate of 10.2 kc/s phaseshifter 60 and applies this rotation through gears 78 and 80 to oneinput of differential 82. In addition, shaft 76 is coupled to shaft 66through gears 84, 86, 88, and 90. At the same time, motor 58 drivesshaft 92 at a rate of 20 times the rate of 10.2 kc/s phase shifter 60and applies this rotation through gears 94 and 96 to the second input ofdifferential 82. In addition, shaft 92 is coupled to shaft 74 throughgears 98 and 100. Differential 82, then, drives input shaft 102 ofindicator 68 to indicate the arrival time of the composite signal fromOmega station A. If desired, input shaft 66 of the motor-phase-shifterunit for Omega station A may be coupled, through gears 104, 106, and 108and differential 110, with the corresponding shaft of themotor-phase-shifter unit for Omega station B to cause input shaft 1 12of indicator 68 to indicate the phase difference between the 10.2 kc/ssignals from Omega stations A and B. Similarly, shaft 74 of themotor-phaseshifter unit for Omega station A can be coupled, throughgears 114, 116, and 118 and differential 120, with the correspondingshaft of the motor-phase-shifter unit for Omega station E to cause inputshaft 122 of indicator 68 to indicate the phase difference between the13.6 kc/s signals from Omega stations A and B. Moreover, shaft 102 ofthe motor-phase-shifter unit in Omega station A can be coupled, throughgears 124, 126, and 128 and differential 130, with the correspondingshaft of the motor-phase-shifter unit for Omega station B to cause inputshaft 132 of indicator 68 to indicate the phase difference between thecomposite signals from Omega stations A and B.

In use, the apparatus of the present invention receives the 10.2 kc/sand 13.6 kc/s signals transmitted by each of the Omega transmittingstations and compares these signals with a local reference to provide anindication of the arrival time of each of these signals. In addition,the device of the present invention processes these signals to determinethe arrival time of the composite signal. Since the velocity ofpropagation of each of these signals is substantially constant, thecomputer or the navigator can readily employ the data thus provided todetermine the differences of the distances to the respective Omegastations and, hence, can determine the navigators position quickly andaccurately.

Although the examples cited herein have applied specifically to thefrequency pair 10.2 and 13.6 kc/s, the method is clearly applicable toother pairs of frequencies, with suitable adjustment of the constant m,as shown in Equation l l or by experiment.

Furthermore, if three or more frequencies are received from eachtransmitting station, three or more composite signals can be measured.It is then easy to provide means to present to the operator an averageor a weighted average of these several results, with correspondingimprovement in the accuracy and reliability of the final result. Allsuch multiple comparisons are within the teachings of the presentinvention.

Obviously, numerous variations and modifications can be made withoutdeparting from the present invention. Accordingly, it should be clearlyunderstood that the form of the present invention described above andshown in the accompanying drawing is illustrative only and is notintended to limit the scope of the invention.

What is claimed is:

1. A method of navigation comprising the steps of:

broadcasting time-shared radio signals at a plurality of knownfrequencies from each of a plurality of synchronized transmitterslocated at widely separated positions about the earth; establishing alocal-time reference signal at a receiving station whose position is tobe determined;

detecting the arrival at said receiving station of the signal at a firstfrequency from a first of said transmitters;

comparing the phase of said signal at said first frequency from saidfirst transmitter with the local-time reference signal to determine thetransmission time of said first frequency signal from said firsttransmitter to said receiving station;

detecting the arrival at said receiving station of the signal at asecond frequency from said first transmitter;

comparing the phase of said signal at said second frequency from saidfirst transmitter with the local-time reference signal to determine thetransmission time of said signal at said second frequency from saidfirst transmitter to said receiving station;

combining said signals at said first and second frequencies from saidfirst transmitter to derive a first composite signal having atransmission time from said first transmitter to said receiving stationdefined by giving preselected weight, respectively, to the average ofthe transmission times of said signals from said first transmitter andthe transmission time from said first transmitter of the differencefrequency between said first and second frequencies;

detecting the arrival at said receiving station of the signal at saidfirst frequency from a second of said transmitters;

comparing the phase of said signal at said first frequency from saidsecond transmitter with the local-time reference signal to determine thetransmission time of said first frequency signal from said secondtransmitter to said receiving station;

detecting the arrival at said receiving station of the signal at saidsecond frequency from said second transmitter;

comparing the phase of said signal at said second frequency from saidsecond transmitter with the local-time reference signal to determine thetransmission time of said second frequency signal from said secondtransmitter to said receiving station;

combining said signals from said second transmitter to derive a secondcomposite signal having a trans mission time from said secondtransmitter to said receiving station defined by giving preselectedweight, respectively, to the average of the transmission times of saidsignals from said second transmitter and the transmission time from saidsecond transmitter of the difference frequency between said first andsecond frequencies;

detecting the arrival at said receiving station of the signal at saidfirst frequency from a third of said transmitters;

comparing the phase of said signal at said first frequency from saidthird transmitter with the local-time reference signal to determine thetransmission time of said first frequency signal from said thirdtransmitter to said receiving station;

detecting the arrival at said receiving station of the signal at saidsecond frequency from said third transmitter;

comparing the phase of said signal at said second frequency from saidthird transmitter with the local-time reference signal to determine thetransmission time of said second frequency signal from said thirdtransmitter to said receiving station;

combining said signals from said third transmitter to derive a thirdcomposite signal having a transmission time from said third transmitterto said receiving station defined by giving preselected weight,respectively, to the average of the transmission time of said signalsfrom said third transmitter and the transmission time from said thirdtransmitter of the difference frequency between said first and secondfrequencies; and

plotting the position of said receiving station as a function of thetransmission times and velocities of propagation of said compositesignals.

2. The method of claim 1 wherein said plotting step comprises:

plotting the position of said receiving station with respect to saidfirst transmitter as a function of the transmission time and velocity ofpropagation of said first composite signal;

plotting the position of said receiving station with respect to saidsecond transmitter as a function of the transmission time and velocityof propagation of said second composite signal; and

plotting the position of said receiving station with respect to saidthird transmitter as a function of the transmission time and velocity ofpropagation of said third composite signal.

3. The method of claim 1 wherein said plotting step comprises:

plotting a first position line as a function of the differences betweenthe transmission times of said first and second complete signals; and

plotting a second position line as a function of the differences betweenthe transmission times of said second and third composite signals.

4. The method of claim 1 wherein said combining steps require that thesignals at said first and second frequencies from the respectivetransmitters be combined according to the relationship where Tctransmission time of the composite signal T transmission time of thelower frequency signal T transmission time of the higher frequencysignal and m is a constant having a value which is a function of saidhigher and lower frequencies.

5. The method of claim 4 wherein:

where f, the higher frequency and f the lower frequency.

6. The method of claim wherein:

m has a value in the range from 2.0 to 5.0.

7. The method of claim 1 wherein the velocity of propagation of thecomposite signals is determined by the relationship (c/v) l (h/3a) wherec the velocity of light v the velocity of propagation of the compositesignal h the height of the ionosphere layer a the radius of the earth1A. 8. The method of claim 1 wherein said first and second frequenciesare very low radio frequencies.

9. The method of claim 1 wherein said first frequency is 10.2 kilocyclesper second; and said second frequency is 13.6 kilocycles per second.

10. A method of navigation comprising the steps of: broadcastingtime-shared radio signals at a plurality of known frequencies from eachof a plurality of carefully synchronized transmitters locatedat widelyseparated positions about the earth;

establishing an accurate, local-time reference signal at a receivingstation whose position is to' be determined;

detecting the arrival at said receiving station of the signal at a firstfrequency from a first of said transmitters; comparing the phase of saidsignal at said first frequency from said first transmitter with thelocal-time reference signal to determine the transmission time of saidfirst frequency signal from said first transmitter to said receivingstation;

detecting the arrival at said receiving station of the signal at asecond frequency from said first transmitter;

comparing the phase of said signal at said second frequency from saidfirst transmitter with the local-time reference signal to determine thetransmission time of said signal at said second frequency from saidfirst transmitter to said receiving station;

combining said signals at said first and second frequencies from saidfirst transmitter to derive a first composite signal having atransmission time from said first transmitter to said receiving stationdefined by giving preselected weight, respectively, to the average ofthe transmission times of said signals from said first transmitter andthe transmission time from said first transmitter of the differencefrequency between said first and second frequencies;

detecting the arrival at said receiving station of the signal at saidfirst frequency from a second of said transmitters;

comparing the phase of said signal at said first frequency from saidsecond transmitter with the local-time reference signal to determine thesecond transmission time of said first frequency signal from said secondtransmitter to said receiving station;

detecting the arrival at said receiving station of the signal at saidsecond frequency from said second transmitter;

comparing the phase of said signal at said second frequency from saidsecond transmitter with the local-time reference signal to determine thetransmission time of said second frequency signal from said secondtransmitter to said receiving station; combining said signals from saidsecond transmitter to derive a second composite signal having atransmission time from said second transmitter to said receiving stationdefined by giving preselected weight, respectively, to the average ofthe transmission times of said signals from said second transmitter andthe transmission time from said second transmitter of the differencefrequency between said first and second frequencies; and

plotting the position of said receiving station as a function of thetransmission times and velocities of propagation of said compositesignals.

11. A method of navigation from broadcasted timeshared radio signals ata plurality of known frequencies from each of a plurality ofsynchronized transmitters located at separated positions about theearth, comprising the steps of:

detecting the arrival of a first signal at a first frequency from afirst of said transmitters at a receiving station whose position is tobe determined;

comparing the phase of the first signal with a localtime referencesignal to determine the transmission time of the first frequency signalfrom said first transmitter to the receiving station,

detecting the arrival of a second signal at a second frequency from saidfirst transmitter at the receiving station;

comparing the phase of the second signal with the localtime referencesignal to determine the transmission time of the second frequency signalfrom said first transmitter to the receiving station;

combining the first and second signals to derive a first compositesignal having a transmission time from said first transmitter to thereceiving station defined by giving preselected weight, respectively, tothe average of the transmission times of the first and second signalsfrom said first transmitter and the transmission time from said firsttransmitter of the difference frequency between the first and secondfrequency signals;

detecting the arrival of a third signal at the first frequency from asecond of said transmitters at the receiving station; comparing thephase of the third signal with the local-time reference signal todetermine the transmission time of the first frequency signal from saidsecond transmitter to the receiving station;

detecting the arrival of a fourth signal at the second frequency fromsaid second transmitter at the receiving station;

comparing the phase of the fourth signal with the local-time referencesignal to determine the transmission time of the second frequency signalfrom said second transmitter to the receiving station;

combining the third and fourth signals to derive a second compositesignal having a transmission time from said second transmitter to thereceiving station defined by giving preselected weight, respectively, tothe average of transmission times of the third and fourth signals fromsaid second transmitter and the transmission time from said secondtransmitter of the difference frequency between the third and fourthsignals; and

generating the position of the receiving station as a function of thetransmission times and the velocities of propagation of said compositesignals.

12. Apparatus for radio navigation with a plurality of synchronizedtransmitters located at widely-separated positions about the earth eachbroadcasting timeshared radio signals at a plurality of knownfrequencies, the combination comprising:

antenna means located at a receiving station whose position is to bedetermined for detecting the signals broadcast by said transmitters;

time reference means establishing a local-time reference signal;

phase-comprising means connected to said antenna and said time referencemeans for comparing the phase of signals detected by said antenna withsaid local-time reference signal to determine the transmission times ofthe respective signals detected by said antenna from the correspondingone of said transmitters;

computer means connected to receive the output of said phase-comparingmeans and operative to combine the signals at first and secondfrequencies from each respective transmitter to derive a compositesignal for each respective transmitter having a transmission time fromthe respective transmitter to said receiving station defined by givingpreselected weight, respectively, to the average of the transmissiontimes of the signals at said first and second frequencies from saidrespective transmitter and the transmission time from said respectivetransmitter of the difference frequency between said first and secondfrequencies; and

display means for providing a visual indication of said transmissiontimes.

13. Apparatus for radio navigation by use of a plurality of synchronizedtransmitters located at separated positions about the earth eachbroadcasting timeshared radio signals at a plurality of knownfrequencies, the combination which comprises:

means for detecting the arrival of a first signal at a first frequencyfrom a first of said transmitters at a receiving station whose positionis to be determined;

means for comparing the phase of the first signal with a local-timereference signal to determine the transmission time of the first signalfrom said first transmitter to the receiving station;

means for detecting the arrival of a second signal at a second frequencyfrom said first transmitter at the receiving station;

means for comparing the phase of the second signal with the local-timereference signal to determine the transmission time of the second signalfrom said first transmitter to the receiving station;

means for combining the first and second signals to derive a firstcomposite signal having a transmission time from said first transmitterto the receiving station defined by giving preselected weight,respectively, to the average of the transmission times of the first andsecond signals from said first transmitter and the transmission timefrom said first transmitter of the difference frequency between thefirst and second signals;

means for detecting the arrival of a third signal at the first frequencyfrom a second of said transmitters at the receiving station;

means for comparing the phase of the third signal with the local-timereference signal to determine the transmission time of the third signalfrom said second transmitter to the receiving station;

means for detecting the arrival of a fourth signal at the secondfrequency from said second transmitter at the receiving station;

means for comparing the phase of the fourth signal with the local-timereference signal to determine the transmission time of the fourth signalfrom said second transmitter to the receiving station;

frequency between third and fourth signals; and

display means for providinga visual indication of said first and secondcomposite signals from which the position of the receiving station as afunction of the transmission times and velocities of propagation can becalculated from said composite signals.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent N 3.696.424Dated October 3. 1972 Inven JOHN A. PIERCE It is certified that errorappears in the aboveidentified patent and that said Letters Patent arehereby corrected as shown below:

On the cover sheet the name of the Assignee should.

read American Standard Inc. a corporation of Delaware Column 13, line 32after "second", cancel "complete",

and insert composite column 16, line 1,

"phase-comprising" should read phase-comparing Signed and sealed thislst day of May 1973.

(SEAL) Atte'st:

EDWARD M.FLETCHER,JR. ROBERT GOTTSCHALK Attesting Officer a.Commissioner of Patents FORM PO-1G50(10-69) USCOMM-DC 6087 G-PGQ fi'U.S. GOVERNMENT PRINTING OFFICE: 1969 O-366334,,

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTTON Patent 3,696.424Dated October 3 L 1972 Inventor(s) JOHN A. PIERCE It is certified thaterror appears in the above-identified patent and that said LettersPatent are hereby corrected as shown below:

On the cover sheet the name of the Assignee should read AmericanStandard Inc., a corporation of Delaware Column 13, line 32, after"second", cancel "complete",

and insert composite column 16, line 1, V

"phase-comprising" should read phase-comparing Signed and sealed thislst day of May 1973.

(SEAL Atte'st:

EDWARD M.FLETCHER,JR. ROBERT GOTTSCHALK Attesting Officer Commissionerof Patents FORM PEI-I050 (10-69) USCOMM-DC 60376-P69 fi U45. GOVERNMENTPRINTING OFFICE: I969 O366-334,

1. A method of navigation comprising the steps of: broadcastingtime-shared radio signals at a plurality of known frequencies from eachof a plurality of synchronized transmitters located at widely-separatedpositions about the earth; establishing a local-time reference signal ata receiving station whose position is to be determined; detecting thearrival at said receiving station of the signal at a first frequencyfrom a first of said transmitters; comparing the phase of said signal atsaid first frequency from said first transmitter with the local-timereference signal to determine the transmission time of said firstfrequency signal from said first transmitter to said receiving station;detecting the arrival at said receiving station of the signal at asecond frequency from said first transmitter; comparing the phase ofsaid signal at said second frequency from said first transmitter withthe local-time reference signal to determine the transmission time ofsaid signal at said second frequency from said first transmitter to saidreceiving station; combining said signals at said first and secondfrequencies from said first transmitter to derive a first compositesignal having a transmission time from said first transmitter to saidreceiving station defined by giving preselected weight, respectively, tothe average of the transmission times of said signals from said firsttransmitter and the transmission time from said first transmitter of thedifference frequency between said first and second frequencies;detecting the arrival at said receiving station of the signal at saidfirst frequency from a second of said transmitters; comparing the phaseof said signal at said first frequency from said second transmitter withthe local-time reference signal to determine the transmission time ofsaid first frequency signal from said second transmitter to saidreceiving station; detecting the arrival at said receiving station ofthe signal at said second frequency from said second transmitter;comparing the phase of said signal at said second frequency from saidsecond transmitter with the local-time reference signal to determine thetransmission time of said second frequency signal from said secondtransmitter to said receiving station; combining said signals from saidsecond transmitter to derive a second composite signal having atransmission time from said second transmitter to said receiving stationdefined by giving preselected weight, respectively, to the average ofthe transmission times of said signals from said second transmitter andthe transmission time from said second transmitter of the differencefrequency between said first and second frequencies; detecting thearrival at said receiving station of the signal at said first frequencyfrom a third of said transmitters; comparing the phase of said signal atsaid first frequency from said third transmitter with the local-timereference signal to determine the transmission time of said firstfrequency signal from said third transmitter to said receiving station;detecting the arrival at said receiving station of the signal at saidsecond frequency from said third transmitter; comparing the phase ofsaid signal at said second frequency from said third transmitter withthe local-time reference signal to determine the transmission time ofsaid second frequency signal from said third transmitter to saidreceiving station; combining said signals from said third transmitter toderive a third composite signal having a transmission time from saidthird transmitter to said receiving station defined by givingpreselected weight, respectively, to the average of the transmissiontime of said signals from said third transmitter and the transmissiontime from said third transmitter of the difference frequency betweensaid first and second frequencies; and plotting the position of saidreceiving station as a function of the transmission times and velocitiesof propagation of said composite signals.
 2. The method of claim 1wherein said plotting step comprises: plotting the position of saidreceiving station with respect to said first transmitter as a functionof the transmission time and velocity of propagation of said firstcomposite signal; plotting the position of said receiving station withrespect to said second transmitter as a function of the transmissiontime and velocity of propagation of said second composite signal; andplotting the position of said receiving station with respect to saidthird transmitter as a function of the transmission time and velocity ofpropagation of said third composite signal.
 3. The method of claim 1wherein said plotting step comprises: plotting a first position line asa function of the differences between the transmission times of saidfirst and second complete signals; and plotting a second position lineas a function of the differences between the transmission times of saidsecond and third composite signals.
 4. The method of claim 1 whereinsaid combining steps require that the signals at said first and secondfrequencies from the respective transmitters be combined according tothe relationship To T1 + m (T2 - T1) where Tc transmission time of thecomposite signal T1 transmission time of the lower frequency signal T2transmission time of the higher frequency signal and m is a constanthaving a value which is a function of said higher and lower frequencies.5. The method of claim 4 wherein: where f2 the higher frequency and f1the lower frequency.
 6. The method of claim wherein: m has a value inthe range from 2.0 to 5.0.
 7. The method of claim 1 wherein the velocityof propagation of the composite signals is determined by therelationship (c/v) 1 + (h/3a) where c the velocity of light v thevelocity of propagation of the composite signal h the height of theionosphere layer a the radius of the earth
 8. The method of claim 1wherein said first and second frequencies are very low radiofrequencies.
 9. The method of claim 1 wherein said first frequency is10.2 kilocycles per second; and said second frequency is 13.6 kilocyclesper second.
 10. A method of navigation comprising the steps of:broadcasting time-shared radio signals at a plurality of knownfrequencies from each of a plurality of carefully synchronizedtransmitters located at widely separated positions about the earth;establishing an accurate, local-time reference signal at a receivingstation whose position is to be determined; detecting the arrival atsaid receiving station of the signal at a first frequency from a firstof said transmitters; comparing the phase of said signal at said firstfrequency from said first transmitter with the local-time referencesignal to determine the transmission time of said first frequency signalfrom said first transmitter to said receiving station; detecting thearrival at said receiving station of the signal at a second frequencyfrom said first transmitter; comparing the phase of said signal at saidsecond frequency from said first transmitter with the local-timereference signal to determine the transmission time of said signal atsaid second frequency from said first transmitter to said receivingstation; combining said signals at said first and second frequenciesfrom said first transmitter to derive a first composite signal having atransmission time from said first transmitter to said receiving stationdefined by giving preselected weight, respectively, to the average ofthe transmission times of said signals from said first transmitter andthe transmission time from said first transmitter of the differencefrequency between said first and second frequencies; detecting thearrival at said receiving station of the signal at said first frequencyfrom a second of said transmitters; comparing the phase of said signalat said first frequency from said second transmitter with the local-timereference signal to determine the second transmission time of said firstfrequency signal from said second transmitter to said receiving station;detecting the arrival at said receiving station of the signal at saidsecond frequency from said second transmitter; comparing the phase ofsaid signal at said second frequency from said second transmitter withthe local-time reference signal to determine the transmission time ofsaid second frequency signal from said second transmitter to saidreceiving station; combining said signals from said second transmitterto derive a second composite signal having a transmission time from saidsecond transmitter to said receiving station defined by givingpreselected weight, respectively, to the average of the transmissiontimes of said signals from said second transmitter and the transmissiontime from said second transmitter of the difference frequency betweensaid first and second frequencies; and plotting the position of saidreceiving station as a function of the transmission times and velocitiesof propagation of said composite signals.
 11. A method of navigationfrom broadcasted time-shared radio signals at a plurality of knownfrequencies from each of a plurality of synchronized transmitterslocated at separated positions about the Earth, comprising the steps of:detecting the arrival of a first signal at a first frequency from afirst of said transmitters at a receiving station whose position is tobe determined; comparing the phase of the first signal with a local-timereference signal to determine the transmission time of the firstfrequency signal from said first transmitter to the receiving station,detecting the arrival of a second signal at a second frequency from saidfirst transmitter at the receiving station; comparing the phase of thesecond signal with the local-time reference signal to determine thetransmission time of the second frequency signal from said firsttransmitter to the receiving station; combining the first and secondsignals to derive a first composite signal having a transmission timefrom said first transmitter to the receiving station defined by givingpreselected weight, respectively, to the average of the transmissiontimes of the first and second signals from said first transmitter andthe transmission time from said first transmitter of the differencefrequency between the first and second frequency signals; detecting thearrival of a third signal at the first frequency from a second of saidtransmitters at the receiving station; comparing the phase of the thirdsignal with the local-time reference signal to determine thetransmission time of the first frequency signal from said secondtransmitter to the receiving station; detecting the arrival of a fourthsignal at the second frequency from said second transmitter at thereceiving station; comparing the phase of the fourth signal with thelocal-time reference signal to determine the transmission time of thesecond frequency signal from said second transmitter to the receivingstation; combining the third and fourth signals to derive a secondcomposite signal having a transmission time from said second transmitterto the receiving station defined by giving preselected weight,respectively, to the average of transmission times of the third andfourth signals from said second transmitter and the transmission timefrom said second transmitter of the difference frequency between thethird and fourth signals; and generating the position of the receivingstation as a function of the transmission times and the velocities ofpropagation of said composite signals.
 12. Apparatus for radionavigation with a plurality of synchronized transmitters located atwidely-separated positions about the earth each broadcasting time-sharedradio signals at a plurality of known frequencies, the combinationcomprising: antenna means located at a receiving station whose positionis to be determined for detecting the signals broadcast by saidtransmitters; time reference means establishing a local-time referencesignal; phase-comprising means connected to said antenna and said timereference means for comparing the phase of signals detected by saidantenna with said local-time reference signal to determine thetransmission times of the respective signals detected by said antennafrom the corresponding one of said transmitters; computer meansconnected to receive the output of said phase-comparing means andoperative to combine the signals at first and second frequencies fromeach respective transmitter to derive a composite signal for eachrespective transmitter having a transmission time from the respectivetransmitter to said receiving station defined by giving preselectedweight, respectively, to the average of the transmission times of thesignals at said first and second frequencies from said respectivetransmitter and the transmission time from said respective transmitterof the difference frequency between said first and second frequencies;and display means for providing a visual indication of said transmissiontimes.
 13. Apparatus for radio navigation by use of a plurality ofsynchronized transmitters located at separated positions about the eartheach broadcasting time-shAred radio signals at a plurality of knownfrequencies, the combination which comprises: means for detecting thearrival of a first signal at a first frequency from a first of saidtransmitters at a receiving station whose position is to be determined;means for comparing the phase of the first signal with a local-timereference signal to determine the transmission time of the first signalfrom said first transmitter to the receiving station; means fordetecting the arrival of a second signal at a second frequency from saidfirst transmitter at the receiving station; means for comparing thephase of the second signal with the local-time reference signal todetermine the transmission time of the second signal from said firsttransmitter to the receiving station; means for combining the first andsecond signals to derive a first composite signal having a transmissiontime from said first transmitter to the receiving station defined bygiving preselected weight, respectively, to the average of thetransmission times of the first and second signals from said firsttransmitter and the transmission time from said first transmitter of thedifference frequency between the first and second signals; means fordetecting the arrival of a third signal at the first frequency from asecond of said transmitters at the receiving station; means forcomparing the phase of the third signal with the local-time referencesignal to determine the transmission time of the third signal from saidsecond transmitter to the receiving station; means for detecting thearrival of a fourth signal at the second frequency from said secondtransmitter at the receiving station; means for comparing the phase ofthe fourth signal with the local-time reference signal to determine thetransmission time of the fourth signal from said second transmitter tothe receiving station; means for combining the third and fourth signalsto derive a second composite signal having a transmission time from saidsecond transmitter to the receiving station defined by givingpreselected weight, respectively, to the average of the transmissiontime signals of the frequency signals from said second transmitter andthe transmission time from said second transmitter of the differencefrequency between third and fourth signals; and display means forproviding a visual indication of said first and second composite signalsfrom which the position of the receiving station as a function of thetransmission times and velocities of propagation can be calculated fromsaid composite signals.